Topology Seminar (Main Talk): Random Knots from Petal Diagrams

Seminar | October 17 | 4-5 p.m. | 3 Evans Hall

 Chaim Even Zohar, UC Davis

 Department of Mathematics

The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and arises also in applications to the natural sciences. We will discuss knots that arise from random permutations using petal projections (Adams et al. 2012). We will explain why the probability of obtaining any given knot type in this model is positive if the number of petals is at least linear in the knot's crossing number, and why it decays to zero as this number grows to infinity. Our approach uses different knot invariants and arguments than those that have been used in other random models.

Joint work with Joel Hass, Nati Linial, and Tahl Nowik.